针对所有 $$k>4$$ 的列表-k-着色无 H 图

IF 1 2区数学 Q1 MATHEMATICS

Combinatorica Pub Date : 2024-05-14 DOI:10.1007/s00493-024-00106-2

Maria Chudnovsky, Sepehr Hajebi, Sophie Spirkl

{"title":"针对所有 $$k>4$$ 的列表-k-着色无 H 图","authors":"Maria Chudnovsky, Sepehr Hajebi, Sophie Spirkl","doi":"10.1007/s00493-024-00106-2","DOIUrl":null,"url":null,"abstract":"Given an integer \$k>4\$ and a graph H, we prove that, assuming P\$\\ne \$ NP, the List-k -Coloring Problem restricted to H-free graphs can be solved in polynomial time if and only if either every component of H is a path on at most three vertices, or removing the isolated vertices of H leaves an induced subgraph of the five-vertex path. In fact, the “if” implication holds for all \$k\\ge 1\$.\n","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"List-k-Coloring H-Free Graphs for All $$k>4$$\",\"authors\":\"Maria Chudnovsky, Sepehr Hajebi, Sophie Spirkl\",\"doi\":\"10.1007/s00493-024-00106-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given an integer \\\$k>4\\\$ and a graph H, we prove that, assuming P\\\$\\\\ne \\\$ NP, the List-k -Coloring Problem restricted to H-free graphs can be solved in polynomial time if and only if either every component of H is a path on at most three vertices, or removing the isolated vertices of H leaves an induced subgraph of the five-vertex path. In fact, the “if” implication holds for all \\\$k\\\\ge 1\\\$.\\n\",\"PeriodicalId\":50666,\"journal\":{\"name\":\"Combinatorica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-05-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Combinatorica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00493-024-00106-2\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Combinatorica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00493-024-00106-2","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

给定一个整数$k>4$和一个图H，我们证明，假设P$\ne $ NP，当且仅当H的每个分量都是最多三个顶点上的路径，或者去除H的孤立顶点会留下一个五顶点路径的诱导子图时，局限于无H图的List-k -Coloring Problem可以在多项式时间内求解。事实上，"如果 "的蕴含对于所有的 $k\ge 1$ 都成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

List-k-Coloring H-Free Graphs for All $$k>4$$

查看原文本刊更多论文

List-k-Coloring H-Free Graphs for All $$k>4$$

Given an integer $k>4$ and a graph H, we prove that, assuming P$\ne $ NP, the List-k -Coloring Problem restricted to H-free graphs can be solved in polynomial time if and only if either every component of H is a path on at most three vertices, or removing the isolated vertices of H leaves an induced subgraph of the five-vertex path. In fact, the “if” implication holds for all $k\ge 1$.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are - Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups). - Combinatorial optimization. - Combinatorial aspects of geometry and number theory. - Algorithms in combinatorics and related fields. - Computational complexity theory. - Randomization and explicit construction in combinatorics and algorithms.